# Utvrđivanje indikatora uspješnosti studiranja

Zorko, Mislav (2015) Utvrđivanje indikatora uspješnosti studiranja. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

In this thesis we look at a sample of students who enrolled in the study of mathematics in the period from 2005 to 2011. The sample is split into two parts, the first before the introduction of the state graduation and the other after. In the first sample there is a change in computer courses, while the second sample has the same courses over the years. We have defined the concept of a successful student as a student who has passed all courses in the first year of the term. Thesis consists of five chapters. In the first chapter we provide descriptive statistics of the sample. We concluded that there was no statistically significant difference (significance level is $\alpha = 0.05$) between the generation that listened to various computer courses and we assumed that in the sample courses are the same through the years. Furthermore, we analyzed the first variable, points from high school ($\mathcal{BS}$), and then points to the entrance examination/State graduation (($\mathcal{BT}$). With bar charts, box-plots and tables with basic properties, we conducted a test of analysis of variance (ANOVA). In the case where there was a statistically significant difference (significance level is $\alpha = 0.05$) between at least two groups, we conducted further Tukey test and the results are given in the tables. At the end of the first chapter we conduct an analysis of successful students. We looked at the share of successful students over the years and at individual courses. With graphics and basic tables, we conducted tests of proportions. All results are presented in tables. The second and third chapter gives the theoretical aspect of the logistic regression. An introduction to univariate and multivariate analysis is given and main concepts are defined. There is also a background of adapting logistic regression model and testing the significance of the coefficients with three tests: likelihood ratio test, Wald test and Score test. At the end of the chapter we give background of estimation of confidence intervals. The fourth chapter provides the application of basic univariate and multivariate logistic regression model to the observed sample of students. We looked at the impact of the independent variables $\mathcal{BS}$ and $\mathcal{BT}$ on the dependent dichotomous variable success ($\mathcal{US}$). We concluded that there is a link between student success and the observed independent variables. Using the ROC curve, we have concluded that the independent variable $\mathcal{BT}$ is better in assessing the success of the independent variables $\mathcal{BS}$, but that it is optimally to use multivariate model that includes both variables. In addition to the standard tests and tables, we give graphical representations of logistics functions with $95\%$ stripes reliability and associated ROC curve. We conducted the corresponding Wald test for the significance of the coefficients and concluded that in all univariate and multivariate models observed independent variables are significant. We also looked at part of the sample of students who have passed all courses in the first semester. All model variables were significant (significance level $\alpha = 0.05$). In the last chapter we give a general algorithm for estimating parameters of multivariate models. There is also an implementation of the code in the programming language Matlab.